Macro-scale demonstration of Kahneman & Tversky’s Conjunction Fallacy

Following the death of the great Daniel Kahneman.

In 2010 I reached out to Daniel Kahneman — my only personal interaction with him — for his opinion on the peculiar macro-scale demonstration of the Conjunction Fallacy (or CF, sometimes also known as the Linda Problem), which I noticed to have taken place in Israel in the debate about a proposal to amend Israel’s naturalization oath. 

Background

The CF, at its core, is the idea that the more detailed a description is, the less likely it is true.

Compare:

  1. Trump is a former U.S. president.
  2. Trump is a former U.S. president who broke his oath of office.
  3. Trump, a former U.S. president who broke his oath of office, is not a patriot.
  4. …

The more information you provide on something, the more you are running the risk of misrepresenting it— or representing your personal take: shifting from a presumably factual to an opinionated or personal description.

In terms of truth, silence is the best strategy. That’s also the rationale behind narrative minimalism.

(Wovon man nicht sprechen kann, darüber muss man schweigen?)

From individual to group decision-making

Conceptually and experimentally, the CF refers to individual decision-making. 

How to meaningfully extend it to a group, as a manifestation of collective decision-making or individual decision-making in a group context? 

Instead of a direct answer, consider not an experiment but an actual event taking place over a decade ago that exhibited a CF pattern: the controversy over a bill purporting to amend Israel’s naturalization oath.  

Israel’s original 1952 naturalization law prescribes an oath to be taken by the prospective citizen: “I declare that I shall be a faithful citizen to the State of Israel.” 

In 2010, a member of parliament attempted to amend that law by appending to the prescribed oath, “…as a Jewish and democratic state.”  

The question divided opinions neatly: the proposal (which did not become law) was supported by right-wingers, opposed by left-wingers, and started a national drama that did not fail to attract considerable international attention. 

The political sentiments, however, would seem misplaced considering that the proposed qualifiers “Jewish” and “democratic” are conditions to be met for the loyalty to be in force. Should Israel not be democratic (or Jewish), the oath taker is to be relieved from the obligation. The more conditions are set out, the less restrictive the oath is— the more liberal it is.  To see that the rationale holds, think how awkward a wedding pledge to be “faithful to you as lovely and beautiful” sounds. (The formulation “You are x and y. I will be faithful to you” would be better, but the uneasy undertone of conditional still lingers.)

Contrary to their intentions, the right-favored amended oath is in fact more progressive than the original formulation (which is still law), which speaks of loyalty to the state without reservation, an uneasy formula for liberal democracies, in which allegiance is routinely made to the constitution, as is the case in the U.S., or to the sovereign, as in the U.K.  The liberal democratic formula is loyalty to the spring of government’s authority rather than to the state, which the government serves.

Practically no person publicly identifying with either side on the question (liberal-minded experts in statistics and in decision-theory were among the outspoken opponents) seemed to form their opinion in accordance with the logical constraints.

Kahneman replied

(I think it’s now fine to publish this private correspondence)

I have not monitored the debate – it makes me sick.  And I don’t want to weigh in on it.  If the wording says Ki-medina Yehudit (I translate from your translation) then you are certainly right, but this is linguistics and I have no special expertise on it.


What to make of it? 

We can explain the macro-scale rationality failure with the simple observation that the oath text was not interpreted as an oath, but as an expression of personal opinion, the answer to the question, “what would you like the object of your loyalty to be?”

This guarantees internal consistency: in the political theater that ensued, both sides played their roles with remarkable consistency and without consequence.  The debate died out; the bill had not become law; no one seemed to care whether the bill would dictate actual policy; no one seemed to care that Israel lacked a naturalization policy and that the naturalization oath, in whatever form, was not —and was not expected to be —administered. 

I wrote at the time in Haaretz on the silly debate: Provisional Loyalty to Provisional State. 

Oath-taking is important 

Oath-taking ties the personal, private and public. I will not write on this fascinating issue here but only mention:

  1. The outstanding Oxford historian Chris Wickham illuminates oath-taking in early medieval Europe as among the legalistic-political inheritance of Rome.
  2. Jewish law differentiates between Neder and Shevua (I will not dwell on the distinction here), or vow and oath.  However, I think the vow-oath distinction in English does not correspond directly to that found in Jewish law. 
  3. But there is a clear parallel between the “modern” oath and the Jewish daily personal commitment to god’s authority upon waking up.
  4. Oath-taking is an enlightened and useful instrument of the U.S. Constitution as I explained here. It is unfortunate, if not at all surprising, that the rationale behind it is not fully appreciated today.  The Federal Government came into force by George Washington’s taking the presidential oath of office on Wall Street on April 30, 1789.  
  5. As far as I know, there is no oath of office in France.  I don’t know the history here, but I noticed that in “Reflections of the French Revolution,” Edmund Burke refers to criticism of the French army whose soldiers, who having taken an oath of loyalty to the king, now had found themselves befuddled as to where to direct their loyalty and purpose.   
  6. The oath of office was a central part in the ascendence and crowning of King Charles III.  It is not less illuminating to consider how the public event was covered by the media and perceived among officials, elected officials and the general public.  As I explained in Haaretz elsewhere, in the 1970s, several newly elected representatives from North Ireland refused the oath of office (loyalty to the queen): they were not allowed to participate in debate and decisions in Parliament. 
  7. While the oath may seem to some as a relic of an era long gone, it is a rather sophisticated instrument that relates freedom and agency.  An oath, as long as it is an oath, is meaningful inasmuch as it is— and is perceived as—a willful expression. John Locke, the prince of common sense, in his Second Treatise of Government writes (chapter 6, Sect. 62) :
    • Commonwealths themselves take notice of, and allow, that there is a time when men are to begin to act like free men, and therefore till that time require not oaths of fealty, or allegiance, or other public owning of, or submission to the government of their countries.

CF enhanced in collective decision-making?

If the oath brouhaha obviously lacks the refinement of a controlled experiment, it suggests that a group setting under certain conditions may enhance the CF effect (irrationality crowds out rationality).  

Learning from the Conjunction Fallacy

I propose next a possible theory to draw from the robustness of the CF effect as demonstrated by the growing and sophisticated body of research since Tversky and Kahneman first reported their findings: in the tradeoff between accuracy and precision, people tend to the latter.  

It is precision that matters, while the CF tweaks accuracy.  

This is rather simple, but “simple truth miscall’d simplicity,” wrote Shakespeare, would have one wish for a restful death.  

Perhaps the precision-vs-accuracy theory could illuminate the easiness/attraction of fake-news.

In more detail:

  1. Statements are assumed heuristically to be accurate, i.e, assumed to be hypothetically and tentatively true as a prerequisite for meaningfulness. They are even mentally edited to support accuracy.
  2.  Asymmetry. No decision or judgment of accuracy is usually needed but a statement would be judged inaccurate only given a compelling reason to do so.
  3. Accuracy is hypothetical, theoretical or tentative: language conjures a reality. Linda never existed, and it never mattered. 
  4. The CF arises because the comparison of different statements in a given context according to their (assumed) accuracy is awkward.
  5. Inherent problem in CF experiment-design. A good experiment design takes pains to place competing statements on similar footing as to minimize variance beyond the detail of interest. This may unwittingly exacerbate the accuracy-problem by suggesting the different experiment statements share context and a background accuracy level. It is not very different from reading one uneven article vs two separate “half” articles: comparison of standards is easier in the latter; we assume a background level of accuracy for a whole piece.
  6. The first moment of meaningfulness is precision.  Accuracy is but a precondition for meaningfulness. In other words: we assume language to be accurate enough, and use it to convey information.